[SCL] Headers and bodies

[Bill Andersen]

Hi, John...

This is all fine.  I really don't care which way it goes except that if 
we go for
method 2, then we need a way to state such syntactic definitions in the 
spec and
I take it that won't come until we do a meta-level.  My wish is purely 
a pragmatic
one - I would like THEN-IF and I'd rather not wait for a meta-CL spec.

On Nov 28, 2003, at 0841, John F. Sowa wrote:

> Bill,
>
> As Pat and I were pointing out, there are two methods
> for defining the semantics of all Boolean operators:
>
>  1. Define all the Boolean operators that anyone would
>     ever need in the semantics.
>
>  2. Define the semantics of some primitive subset of the
>     Boolean operators and let all the others be defined
>     as syntactic combinations of the primitives.
>
> Method #1 is impossible because there are 16 dyadic Boolean
> functions, 256 triadic functions, 65K tetradic functions, etc.
>
> For method #2, it is possible to define all possible Boolean
> functions in terms of some subset of primitives and then
> define the others as syntactic combinations:
>
>  1. The current SCL document defines 5 Boolean functions:
>     one monadic (NOT) and four dyadic (AND, OR, IF-THEN,
>     and EQUIVALENCE).
>
>  2. Other methods use just one primitive (NAND or NOR)
>     or at most two primitives, commonly used combinations
>     of which include (AND and NOT), (OR and NOT), and
>     (IF-THEN and NOT).
>
> My point was that 5 primitives are too many to be elegant
> and too few to be complete (e.g., it omits your request for
> THEN-IF).  I expressed a preference for two (AND and NOT).
>
> Bottom line:  None of these options make any difference in
> the operators that can be included in any concrete language.
>
> John
>
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>
--
Bill Andersen (andersen at ontologyworks.com)
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